Evaluate the definite integral. $\int^{1}_{-1}\left(12\sqrt[3]{x}\right)\,dx = $
First, use the power rule: $\begin{aligned}\int^{1}_{-1}\left(12\sqrt[3]{x}\right)\,dx~&=~\int^{1}_{-1}\left(12x^\frac13\right)\,dx \\&=(9x^\frac43)\Bigg|^{1}_{{-1}}\end{aligned}$ Second, plug in the limits of integration: $[9\cdot{1}^{\frac43}]-[9\cdot({-1})^{\frac43}] = 9-9 = 0$. The answer: $\int^{1}_{-1}\left(12\sqrt[3]{x}\right)\,dx~=~0$